A novel optimized decomposition method for Smoluchowski's aggregation equation

The Smoluchowski's aggregation equation has applications in the field of bio-pharmaceuticals (Zidar et al., 2018 [1]), financial sector (Pushkin et al., 2004 [2]), aerosol science (Shen et al., 2020 [3]) and many others. Several analytical, numerical and semi-analytical approaches have been devised to calculate the solutions of this equation. Semi-analytical methods are commonly employed since they do not require discretization of the space variable. The article deals with the introduction of a novel semi-analytical technique called the optimized decomposition method (ODM) (see Odibat (2020)) to compute solutions of this relevant integro-partial differential equation. The series solution computed using ODM is shown to converge to the exact solution. The theoretical results are validated using numerical examples for scientifically relevant aggregation kernels for which the exact solutions are available. Additionally, the ODM approximated results are compared with the solutions obtained using the Adomian decomposition method (ADM) in Singh et al., (2015). The novel method is shown to be superior to ADM for the examples considered and thus establishes as an improved and efficient method for solving the Smoluchowski's equation. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

The article introduces a new semi-analytical technique, called the optimized decomposition method (ODM), for computing the solutions of the Smoluchowski equation. The superiority of the ODM method in solving this equation is demonstrated through numerical examples.